Question 221175
The measure of angle b, the supplement of angle a, is four times the measure of angle c, the complement of angle a


Step 1.  Supplementary angles means two angles add up to 180 degrees.


Step 2.  Complementary angles means two angles add up to 90 degrees.


Step 3.  Let a be the angle.


Step 4.  Let b=180-a be the supplement of the angle a.


Step 5.  Let c=90-a be the complement of the angle a.


Step 6.  Then  180-a= 4(90-a) the measure of angle b, the supplement of angle a, is four times the measure of angle c, the complement of angle a.


Step 7.  Simplifying Step 6 yields the following steps:


{{{180-a= 360-4a}}}


Add 4a-180 to both sides of the equation to get variable a in left side and numbers on right side.


{{{180-a+4a-180=360-4a+4a-180}}}.


{{{3a=180}}}


Divide 3 to both sides of the equation


{{{3a/3=180/3}}}


{{{a=60}}} {{{180-a=120}}} and {{{90-a=30}}}


Check if equation in Step 6 is true...180-a= 4(90-a) or 120=4*30 which is a true statement.


Step 7.  ANSWER:  Angle is 60 degrees, its supplementary angle is 120 degrees, and its complementary angle is 30 degrees


I hope the above steps and explanation were helpful. 


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Respectfully, 
Dr J